University of Minnesota

Institute of Technology




Course:                 EE 8741 Power Electronics in Power Systems

Term:                   Spring 2002

Professor:             Ned Mohan





High Voltage Direct Current Transmission





Prepared by:         Hans Øverseth Røstøen

                            Igor Borisov









Minneapolis 2002



Table of Contents

Introduction. 3


















Electric power transmission was originally developed with direct current. The availability of transformers and the development and improvement of induction motors at the beginning of the 20th Century, led to greater appeal and use of ac transmission.


Power transmission using HVDC lines is more cost effective than with AC lines, but requires more complicated and expensive interconnections (converters) at each end of the line. The application of HVDC power transmission is therefore limited to transmission of large energies over long distances. Moreover, HVDC is the only practical option when transporting electric energy through cables over long distances. Another special application of HVDC is as a link between AC networks of different frequencies, or between AC networks that become unstable when tied togethter directly. The HVDC link is here short and the term "back-to-back" is used to characterize such a configuration.


Dc transmission became practical when long distances were to be covered or where cables were required. Originally, mercury arc valves were used in the converters. Thyristors were applied in the late 1960’s and solid state valves became a reality. In 1969, a contract for the Eel River dc link in Canada was awarded as the first application of solid state valves for HVDC transmission.

Today, the highest functional d.c. voltage for dc transmission is +/- 600 kV for the 785 km transmission line of the Itaipu scheme in Brazil. Dc transmission is now an integral part of the delivery of electricity in many countries throughout the world.




The level of losses is designed into a transmission system and is regulated by the size of conductor selected. Dc and ac conductors, either as overhead transmission lines or submarine cables can have lower losses but at higher expense since the larger cross-sectional area will generally result in lower losses but cost more. When converters are used for dc transmission in preference to ac transmission, it is generally by economic choice driven by one of the following reasons:


  1. An overhead dc transmission line with its towers can be designed to be less costly per unit of length than an equivalent ac line designed to transmit the same level of electric power. However the dc converter stations at each end are more costly than the terminating stations of an ac line and so there is a breakeven distance above which the total cost of dc transmission is less than its ac transmission alternative. The dc transmission line can have a lower visual profile than an equivalent ac line and so contributes to a lower environmental impact. There are other environmental advantages to a dc transmission line through the electric and magnetic fields being dc instead of ac.


  1. If transmission is by submarine or underground cable, the breakeven distance is much less than overhead transmission. It is not practical to consider ac cable systems exceeding approximately 60 km but dc cable transmission systems are in service whose length is in the hundreds of kilometres and even distances of 600 km or greater have been considered feasible.


  1. Some ac electric power systems are not synchronized to neighbouring networks even though the physical distances between them is quite small. This occurs in Japan where half the country is a 60 Hz network and the other is a 50 Hz system. It is physically impossible to connect the two together by direct ac methods in order to exchange electric power between them. However, if a dc converter station is located in each system with an interconnecting dc link between them, it is possible to transfer the required power flow even though the ac systems so connected remain asynchronous.




The HVDC power converter may be non-controllable if constructed from one or more power diodes in series or controllable if constructed from one or more thyristors in series. The standard bridge or converter connection is defined as a double-way connection comprising six valves or valve arms (six pulse) that are connected as illustrated below. When electric power flows into the dc valve group from the ac system then it is considered a rectifier. If power flows from the dc valvegroup into the ac system, it is an inverter. Each valve consists of many series connected thyristors in thyristor modules.

Figure 1: Electric circuit configuration of the basic six pulse valve group with its converter transformer in star-star connection.








Nearly all HVDC power converters with thyristor valves are assembled in a converter bridge of twelve pulse configuration. The most common twelve pulse configuration is the use of two three phase converter transformers with one dc side winding as an ungrounded star connection and the other a delta configuration. Consequently the ac voltages applied to each six pulse valve group which make up the twelve pulse valve group have a phase difference of 30 degrees which is utilized to cancel the ac side 5th and 7th harmonic currents and dc side 6th harmonic voltage, thus resulting in a significant saving in harmonic filters. Since the voltage rating of thyristors is several kV, a 500 kV system may have hundreds of individual thyristors connected in series.


Figure 2: Twelve pulse valve group configuration with two converter transformers. One transformer in star-star connection and the other transformer in star-delta connection.




The central equipment of a dc substation is the thyristor converter and converter transformer. They may be configured into poles and bipoles. Some dc cable systems only have one pole or “monopole” configuration and may either use the ground as a return path when permitted or use an additional cable to avoid earth currents. Harmonic filters are required on the ac side and usually on the dc side. The characteristic ac side current harmonics generated by 6 pulse converters are 6n +/- 1 and 12n +/- 1 for 12 pulse converters where n equals all positive integers. Ac filters are typically tuned to 11th, 13th, 23rd and 25th harmonics for 12 pulse converters. Tuning to the 5th and 7th harmonics is required if the converters can be configured into 6 pulse operation. Ac side harmonic filters may be switched with circuit breakers or circuit switches to accommodate reactive power requirement strategies since these filters generate reactive power at fundamental frequency. A parallel resonance is naturally created between the capacitance of the ac filters and the inductive impedance of the ac system. For the special case where such a resonance is lightly damped and tuned to a frequency between the 2nd and 4th harmonic, then a low order harmonic filter at the 2nd or 3rd harmonic may be required, even for 12 pulse converter operation.


Figure 3: Monopolar and bipolar configuration.


Characteristic dc side voltage harmonics generated by a 6 pulse converter are of the order 6n and when generated by a 12 pulse converter, are of the order 12n. Dc side filters reduce harmonic current flow on dc transmission lines to minimize coupling and interference to adjacent voice frequency communication circuits. Where there is no dc line such as in the back-to-back configuration, dc side filters may not be required.


Figure 4: Layout of an HVDC substation


Dc reactors are usually included in each pole of a converter station. They assist the dc filters in filtering harmonic currents and smooth the dc side current so that a discontinuous current mode is not reached at low load current operation. Because rate of change of dc side current is limited by the dc reactor, the commutation process of the dc converter is made more robust. Surge arresters across each valve in the converter bridge, across each converter bridge and in the dc and ac switchyard are coordinated to protect the equipment from all overvoltages regardless of their source. They may be used in non-standard applications such as filter protection. Modern HVDC substations use metal-oxide arresters and their rating and selection is made with careful insulation coordination design.









Rectification or inversion for HVDC converters is accomplished through a process known as line or natural commutation. The valves act as switches so that the ac voltage is sequentially switched to always provide a dc voltage. With line commutation, the ac voltage at both the rectifier and inverter must be provided by the ac networks at each end and should be three phase and relatively free of harmonics. As each valve switches on, it will begin to conduct current while the current begins to fall to zero in the next valve to turn off. Commutation is the process of transfer of current between any two converter valves with both valves carrying current simultaneously during this process.


Consider the rectification process. Each valve will switch on when it receives a firing pulse to its gate and its forward bias voltage becomes more positive than the forward bias voltage of the conducting valve. The current flow through a conducting valve does not change instantaneously as it commutates to another valve because the transfer is through transformer windings. The leakage reactance of the transformer windings is also the commutation reactance so long as the ac filters are located on the primary or ac side of the converter transformer. The commutation reactance at the rectifier and inverter is shown as an equivalent reactance XC in the figure below. The sum of all the valve currents transferred the dc side and through the dc reactor is the direct current and it is relatively flat because of the inductance of the dc reactor.


Figure 5: AC voltage and current waveshapes associated with dc converter bridges.


At the inverter, the three phase ac voltage supplied by the ac system provides the forward and reverse bias conditions of each valve in the converter bridge to allow commutation of current between valves the same as in the rectifier. The inverter valve can only turn on and conduct when the positive direct voltage from the dc line is greater than the back negative voltage derived from the ac commutation voltage of the ac system at the inverter.


Reversal of power flow in a line commutated dc link is not possible by reversing the direction of the direct current. The valves will allow conduction in one direction only. Power flow can only be reversed in line commutated dc converter bridges by changing the polarity of the direct voltage. The dual operation of the converter bridges as either a rectifier or inverter is achieved through firing control of the grid pulses.





These converter bridge angles are measured on the three phase valve side voltages and are based upon steady state conditions with a harmonic free and idealized three phase commutation voltage. They apply to both inverters and rectifiers.


Delay angle a. The time expressed in electrical angular measure from the zero crossing of the idealized sinusoidal commutating voltage to the starting instant of forward current conduction. If the angel is less than 90 degrees, the converter bridge is a rectifier and if greater than 90 degrees, it is an inverter.


Advance angle b. The time expressed in electrical angular measure from the starting instant of forward current conduction to the next zero crossing of the idealized sinusoidal commutating voltage. The angle of advance b is related in degrees to the angle of delay a.




Overlap angle m. The duration of commutation between two converter valve arms expressed in electrical angular measure.


Extinction angle g. The time expressed in electrical angular measure from the end of current conduction to the next zero crossing of the idealized sinusoidal commutating voltage. g depends on the angle of advance b and the angle of overlap m.









HVDC transmission systems must transport very large amounts of electric power that can only be accomplished under tightly controlled conditions. Dc current and voltage is precisely controlled to affect the desired power transfer. It is necessary therefore to continuously and precisely measure system quantities that include at each converter bridge, the dc current, its dc side voltage and the delay angle a or for an inverter, its extinction angle g. Two terminal HVDC transmission systems are the more usual and they have in common a preferred mode of control during normal operation. Under steady state conditions, the inverter is assigned the task of controlling the dc voltage. This it may do by maintaining a constant extinction angle g causing the dc voltage Ud to droop with increasing dc current Id as shown in the minimum constant extinction angle g characteristic A-B-C-D. Weaker the ac system is at the inverter; steeper is the droop in Ud. Alternatively, the inverter may normally operate in a dc voltage-controlling mode that is the constant Ud characteristic B-H-E. This means that the extinction angle g must increase beyond its minimum.


Figure 6: Steady state Ud-Id characteristics for a two terminal HVDC system.


If the inverter is operating in a minimum constant g or constant Ud characteristic, the rectifier must control the dc current Id. The steady state constant current characteristic of the rectifier is the vertical section Q-C-H-R. Where the rectifier and inverter characteristic intersect, either at points C or H, is the operating point of the HVDC system.

The operating point can be reached by action of the on-line tap changers of the converter transformers. The inverter must establish the dc voltage Ud by adjusting its on-line tap changer to achieve the desired operating level if it is in constant minimum g control. If in constant Ud control, the on-line tap changer must adjust its tap to allow the controlled level of Ud be achieved with an extinction angle equal to or slightly larger than its minimum setting of 18O in this case.


The on-line tap changers on the converter transformers of the rectifier can be controlled to adjust their tap settings so that the delay angle a has a working range at a level between approximately 10Oand 15Ofor maintaining the constant current setting Iorder. If the inverter is operating in constant dc voltage control at the operating point H, and if the dc current order Iorder is increased so that the operating point H moves towards and beyond point B, the inverter mode of control will revert to constant extinction angle g control and operate on characteristic A-B. Dc voltage Ud will be less than the desired value, and so the converter transformer on-line tap changer at the inverter will boost its dc side voltage until dc voltage control is resumed.


Not all HVDC transmission system controls have a constant dc voltage control such as is depicted by the horizontal characteristic B-H-E. Instead, the constant extinction angle g control of characteristic A-B-C-D and the tap changer will provide the dc voltage control.




Figure 7: Rectifier control loop.



Figure 8: Inverter control loop.

































The d.c. current order Iorder is sent to both the rectifier and inverter. It is usual to subtract a small value of current order from the Iorder sent to the inverter. This is known as the current margin Imargin. The inverter also has a current controller and it attempts to control the dc current Id to the value Iorder - Imargin but the current controller at the rectifier normally overrides it to maintain the dc current at Iorder. This discrepancy is resolved at the inverter in normal steady state operation as its current controller is not able to keep the dc current to the desired value of Iorder - Imargin and is forced out of action. The current control at the inverter becomes active only when the current control at the rectifier ceases when its delay angle a is pegged against its minimum delay angle limit. This is readily observed in the operating characteristics where the minimum delay angle limit at the rectifier is characteristic P-Q. If for some reason or other such as a low ac commutating voltage at the rectifier end, the P-Q characteristic falls below points or E, the operating point will shift from point H to somewhere on the vertical characteristic D-E-F where it is intersected by the lowered P-Q characteristic. The inverter reverts to current control, controlling the dc current Id to the value Iorder - Imargin and the rectifier is effectively controlling dc voltage so long as it is operating at its minimum delay angle characteristic P-Q. The controls can be designed such that the transition from the rectifier controlling current to the inverter controlling current is automatic and smooth.


Figure 9: Dc current controller at an inverter.







During disturbances where the ac voltage at the rectifier or inverter is depressed, it will not be helpful to a weak ac system if the HVDC transmission system attempts to maintain full load current. A sag in ac voltage at either end will result in a lowered dc voltage too. The dc control characteristics shown above indicates the dc current order is reduced if the

dc voltage is lowered. This can be observed in the rectifier characteristic R-S-T and in the inverter characteristic F-G. The controller that reduces the maximum current order is known as a voltage dependent current order limit or VDCOL (sometimes referred to as a VDCL).

The VDCOL control, if invoked by an ac system disturbance will keep the dc current Id to the lowered limit during recovery which aids the corresponding recovery of the dc system. Only when dc voltage Ud has recovered sufficiently will the dc current return to its original Iorder



Figure 10: Modifying the current order with a voltage dependent current order control.





There are a number of special purpose controllers that can be added to HVDC controls to take advantage of the fast response of a dc link and help the performance of the ac system. These include:


Ac system damping controls. An ac. system is subject to power swings due to electromechanical oscillations. A controller can be added to modulate the dc power order or dc current order to add damping. The frequency or voltage phase angle of the ac system is measured at one or both ends of the dc link, and the controller is designed to adjust the power of the dc link accordingly.


Ac system frequency control. A slow responding controller can also adjust the power of the dc link to help regulate power system frequency. If the rectifier and inverter are in asynchronous power systems, the dc controller can draw power from one system to the other to assist in frequency stabilization of each.


Step change power adjustment. A non-continuous power adjustment can be implemented to take advantage of the ability of a HVDC transmission system to rapidly reduce or increase power. If ac system protection determines that a generator or ac transmission line is to be tripped, a signal can be sent to the dc controls to change its power or current order by an amount that will compensate the loss. This feature is useful in helping maintain ac system stability and to ease the shock of a disturbance over a wider area.


Ac undervoltage compensation. Some portions of an electric power system are prone to ac voltage collapse. If a HVDC transmission system is in such an area, a control can be implemented which on detecting the ac voltage drop and the rate at which it is dropping, a fast power or current order reduction of the dc link can be affected. The reduction in power and reactive power can remove the undervoltage stress on the ac system and restore its voltage to normal.


Subsynchronous oscillation damping. A steam turbine and electric generator can have mechanical subsynchronous oscillation modes between the various turbine stages and the generator. If such a generator feeds into the rectifier of a dc link, supplementary control may be required on the dc link to ensure the subsynchronous oscillation modes of concern are positively damped to limit torsional stresses on the turbine shaft.




Power systems are steadily growing with ever-larger capacity. Formerly separated systems are interconnected to each other. Modern power systems have evolved into systems of very large size, stretching out hundreds and thousands of kilometers. With growing generation capacity, different areas in a power system are added with ever-larger inertia.


Furthermore the unbundling of generation, transmission and supply is less oriented towards the physical nature of the synchronously interconnected power systems, which span a large area with interaction among the different sub networks and the power plants. However in the new environment with possible higher loading of the transmission system the network operators may be forced to operate the system closer to its stability limits.


As a consequence in large interconnected power systems small signal stability, especially inter-area oscillations, become an increasing importance. Inter-area oscillation is a common problem in large power systems world-wide. Many electric systems world-wide are experiencing increased loading on portions of their transmission systems, which can, and sometimes do, lead to poorly damped inter-area oscillations. This topic is treated intensively for a long time for those power systems, where the extension of the interconnected systems and/or high transmission load led to stability problems.


High-voltage direct current (HVDC) transmission systems offer a powerful alternative to increase the stability of a power system as well as to improve system operating flexibility. The application of HVDC technology is of special interest to transfer massive amounts of remote hydroelectric power over large distances. In complex interconnected systems, however, the application of this technology to achieve the most effective stabilization of critical inter-area modes requires proper assessment of many interacting factors such as the location of the DC link, the control configuration and the use of modulation controls.


From earlier studies it became apparent that with appropriate control, a DC line could be made to respond more quickly to demands for power flow than could an AC line. Disturbances such as 3-phase faults, sudden load changes, and sudden changes in DC reference current setting were investigated.


Methods of stabilizing an AC system by utilizing a parallel DC line are proposed. Idealized 2-machine system with parallel AC and DC links are considered to establish and evaluate several methods of control, which may be used to improve system stability.


For the case of 1-machine, infinite bus AC-DC system the change in AC power transmitted may be expressed:


, where:


E1, E2 – buses voltages,

       - initial angle between bus voltages,

*     - change in speed of the synchronous machine,

*        - the operator d/dt.


Change in rotor speed due to a small change in accelerating power nay be written:



where H is inertia constant of the machine.


Either a current or a power regulator can control the DC power. Incorporated with this control is a signal dependent upon the change in speed of the machine. Thus, variation from a constant DC power will be determined by a function of Dw, that is:




Making a small change in system power  the change in the rating power can be expressed:



and, using above equations we can express  as:




It is apparent that system damping can be achieved by making  directly proportional to . Moreover,  can be selected so as to define the steady-state operation after a change in Pt has occurred. The change in system power is accepted by the AC system. More important, however, is the fact that with , system damping can be controlled by rating K0. Thus a change in power might be accepted altering the AC transmitted power in a critically damped manner. Since the incorporation of a signal promptly proportional to the change in rotor speed process system damping, it seems logical to include this signal as a part of any proposed .


Steady-state operation is influenced if:




It is apparent that the value of K1 determines the steady-state mode of operation after a change in system power. If, for example, K1 is made large so that






Also, with this type of control, the deviation in the phase angle between bus voltages may be limited during a break in the link (E1E2/X=0) providing the DC system is capable of sustaining the necessary overload.


The phase angle between the bus voltages will return to its value prior to a system disturbance with:




Three basic methods of control can be determined:


Type A           


Type B           


Type C                       


In our investigation we use method Type B.



A simple system is simulated. The system is shown in Figure 11.


Figure 11Simple HVDC circuit model.


A load is being fed from two sources. A HVDC line connects system A to the load. The HVDC control makes the decision of how much power is transferred from system A to the load. System B is producing the power: SB=Sload-SA.


The HVDC model is shown in Figure 12. The valve group system chosen is a six-pulse converter bridge, monopolar configurations. The valve group is a model from the master library in PSCAD/EMTDC.


Figure 12 HVDC model.


The HVDC inverter is normally operating in a dc voltage-controlling mode, the constant Us characteristic B-H-E in Figure 6. If the current order increases, the operating point moves towards and beyond point B. Then the inverter mode of control will revert to constant extinction angle control. The DC voltage will be less than the desired value. When the current order is increased to the operating point where the voltage dependent current order limit will meet the minimum extinction angle characteristic, then the maximum power is transferred in the HVDC line. This can be seen in Figure 13. At the start of the simulation the current order is 0.98 [pu], then the dc voltage is at its maximum. When the current order increases we can see that the voltage is starting decreasing. The control system is now controlling at a minimum extinction angle. At the time 1.9 the voltage dependent current order limit is lower than the current order. The maximum point of power transferred in the HVDC line is reached. The voltage will now be constant again at a lower point then it was in the voltage control mode.


Figure 13 Increase in current order.




The same system is tested for damping control. Now the HVDC line is in parallel with an AC line. System B is changed to a synchronous machine with a multimass model. The model can demonstrate that a HVDC line can damp out oscillations that occur when breakers opens.

Figure 14 System med HVDC line in parallel with the AC line.


At 20 seconds part of the load is disconnected. With no HVDC line, the weak AC line cannot support the load alone. Also in the simulation in Figure 15, the voltage is too low at the load. However, this can be justified with more power thru the HVDC line. In Figure 15 the HVDC line have no control of the damping. The same amount of power is coming out from the HVDC line whatever happens at the load.

Figure 15 System with HVDC line and no damping control.


In Figure 16 the same simulation is done as in Figure 15. The difference is damping control has been applied. It can be seen that the oscillations is smaller in both power and frequency with damping control.


Figure 16 System with HVDC line and damping control.


It can also be seen that the power thru the HVDC line is much less. With damping control the AC line can transfer more power than with no damping control. At 25 seconds the breakers close again. The system then returns back to normal.



HVDC offers powerful alternative to increase stability of a power system as well as to improve system operating flexibility and loss reduction. Our simulations have shown that HVDC lines can be used for oscillations’ damping and improvement of the system stability. When a HVDC line is in parallel with an AC-line, the AC-line can transfer more power because of the damping control. With damping control the AC line can transfer more power than with no damping control.


To keep the losses to a minimum, the control system shall be designed to keep as high voltage as possible. Under steady state conditions, the inverter is assigned to the task of controlling the dc voltage. This can be done by maintaining a constant dc voltage. Alternatively, the inverter may operate at a constant extinction angle g causing the dc voltage to droop with increasing dc current.

If the inverter is operating in a minimum constant g or constant Ud characteristic, the rectifier must control the dc current Id.






  1. Introduction to PSCAD V3 by Dennis Woodford, Manitoba HVDC Research Centre Inc.
  2. HVDC Transmission by Dennis A. Woodford, Manitoba HVDC Research Centre Inc.
  3. Understanding Facts, Concepts and Technology of Flexible AC Transmission System, Narain G. Hingorani, Laszlo Gyugyi,IEEE Power Engineerig Society, IEEE Press.
  4. Power Electronics, Converters, Applications, and Design, Second Edition, Mohan/Undeland/Robbins, John Wiley&Sons Inc
  5. Damping of Low-Frequency Oscillations in Longitudinal Power Systems Using HVDC Modulation and SVCs. J.Arooyo L., A.R. Messina, J.H. Lopez, D.Olguin S. Mexican Council of Science and Technology.
  6. Damping of Interarea Oscillation in Large Interconnected Power Systems. R. Witzmann. Siemens Publication.
  7. Damping of Power Swings in a Parallel AC and DC System. H.A. Peterson, P.C. Krause Jr. IEEE Publication.